Finite Group Databasebeta

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C2×D3×C13×C11⋊C5 #22575110

order8580
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C13×C11⋊C5
unambiguous semidirect productC3⋊(C22×C13×C11⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C13×C11⋊C5)
unambiguous semidirect product(C2×D3×C11)⋊(C5×C13)
unambiguous semidirect product(C2×D3×C11×C13)⋊C5

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C13
HallC3×C13×C11⋊C5 ⋊ C22
HallC2×D3×C11×C13 ⋊ C5
HallC3×C11×C13 ⋊ C22×C5
HallC3×C11⋊C5 ⋊ C22×C13
HallC11×C13 ⋊ C2×C5×D3
HallC2×D3×C11 ⋊ C5×C13
HallC3×C13 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D3×C13
SylowC3 ⋊ C22×C13×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13D3×C11⋊C5
commutator, hypocenterC3×C11C22×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13×D9×C11⋊C5, C2×D3×C13⋊C3×C11⋊C5, D32×C13×C11⋊C5, …
maximal normal subgroup ofC2×D3×C13⋊C3×C11⋊C5, C2×C3×D3×C13×C11⋊C5
maximal quotient ofC2×C13×D9×C11⋊C5, D32×C13×C11⋊C5, C2×C3×D3×C13×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 82);